Degrees are based on the division of a circle into 360 equal parts. One degree is equal to 1/360 of a circle. Degrees are commonly used in everyday life, such as when measuring the temperature in Fahrenheit or the angles of objects in geometry.
Radians are based on the ratio of the length of an arc of a circle to the radius of the circle. One radian is equal to the angle formed by an arc of a circle that is equal in length to the radius of the circle. Radians are commonly used in mathematics and physics, particularly when calculating the properties of circles and spheres.
The relationship between degrees and radians can be expressed as follows:
1 radian = 180/π degrees ≈ 57.2958 degrees
1 degree = π/180 radians ≈ 0.017453 radians
Here are some examples of how degrees and radians are used:
- In geometry, angles are commonly measured in degrees. For example, a right angle is equal to 90 degrees, and a straight angle is equal to 180 degrees.
- In trigonometry, angles are commonly measured in radians. For example, the sine of an angle is defined as the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse, and the cosine of an angle is defined as the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse.
- In physics, angles are commonly measured in radians. For example, the angular velocity of an object is defined as the rate at which the object rotates in radians per second.
In general, degrees are more commonly used in everyday life, while radians are more commonly used in mathematics and physics.